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Appendix Ji

From a study of pp. 4.38 to 442 it will be seen that the Bm
curve is simply the surn of the shear curve, the point of origin of
the former being where Bm = o, viz., at the supports of a girder,
and the outer end of a cantilever. E^ will be a maximum where
shear changes sign, and will decrease with minus shear. In Fig.
816 let Bm increase by 1000 ton-feet over a base of i foot, caused
by a shear of 1000 tons intensity over i foot base; and let a Bm
scale of -Jin. = 1000 ton-feet be proposed. Then ^'= 1000 t.f. =
-j in., b' = i in., y' — 1000 tons — •§• in. x TO, and



= 5m-

The Bm curve can now be drawn, on base N P, by sunimatmg
D L E K F from pole or     Commencing at P, the curve rises to Q

£Ot/v/»/vc'V /A/

the maximum, and then decreases from Q to N, the shear being
minus. These constructions are especially useful for ships. A
curve of weights being drawn, is opposed by a curve of buoyancy
or the weight of water displaced at every section, and the net
result is the load curve, from which shear and Btt may be deduced
as before. Two extreme cases are taken, one with wave crest
amidships, causing 'hogging' strains; and the other with crests
near the ship ends, causing * sagging' strains. Lastly the sections
are treated as built up beams. Fig. 817 is an actual example.